Kesten [1]} showed that the anomalous diffusion occurs on critical percolation on trees and \(Z^2\) . For high-dimensional \(Z^d\) , anomalous diffusion have also obtained for random walks on critical percolation clusters [2]}, [3]}, [4]}. For simplicity, instead of on random clusters, random walks on deterministic regular fractal structures have also been studied. Discrete random walks on Sierpinski gaskets were studied in [5]}, [6]}, [7]} and Brownian motions on Sierpinski gaskets were constructed [8]}, [9]}, [10]}.
